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A Space Allocation Algorithm for Minimal Makespan in Space Scheduling Problems
Abstract
The factory space is one of the critical resources for the machine assembly industry. In machinery industry, space utilizations
are critical to the efficiency of a schedule. The higher the utilization of a schedule is, the quicker the jobs can be done.
Therefore, the main purpose of this research is to derive a method to allocate jobs into the shop floor to minimize the makespan
for the machinery industry. In this research, we develop an algorithm, Longest Contact Edge Algorithm, to schedule jobs into
the shop floor. We employed the algorithm to allocate space for jobs and found that the Longest Contact Edge Algorithm outperforms
the Northwest Algorithm for obtaining better allocations. However, the Longest Contact Edge Algorithm results in more time
complexity than that of the Northwest Algorithm.
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This paper proposes a hybrid metaheuristic for the minimization of makespan in permutation flow shop scheduling problems. The solution approach is robust, fast, and simply structured, and comprises three components: an initial population generation method based on a greedy randomized constructive heuristic, a genetic algorithm (GA) for solution evolution, and a variable neighbourhood search (VNS) to improve the population. The hybridization of a GA with VNS, combining the advantages of these two individual components, is the key innovative aspect of the approach. Computational experiments on benchmark data sets demonstrate that the proposed hybrid metaheuristic reaches high-quality solutions in short computational times. Furthermore, it requires very few user-defined parameters, rendering it applicable to real-life flow shop scheduling problems.
The factory space for assembly is one of critical resources for the machine assembly industry. In the past, many researches discussed job shop or single machine scheduling problems with time constraint. In machinery, factory space constrains scheduling. The most common way for scheduling jobs in machinery industry is to assign jobs based on experience. Therefore, the main purpose of this research is to derive a method to schedule jobs for machinery industry and develop new dispatching rules. In this research, we develop an algorithm, Northwest corner searching algorithm to schedule jobs into the shop floor. In addition, two space dispatching rules, largest space requirement (LSR) and smallest space requirement (SSR), are also developed for sequencing jobs. We find that both the proposed algorithm and dispatching rule perform well in our experiments.
Scheduling has been and continues to be a major issue in production planning. Job shop scheduling is one area where a considerable amount of research has been and continues to be pursued. Usual emphasis is on one machine per work center job shop scheduling. There appears to be very limited literature available on scheduling a job shop problem which requires scheduling of n jobs in m machine centers where each machine center may have k number of identical processors (though the number of identical processors may vary from one machine center to next). We discuss here, the problem of minimize of the makespan for such a job shop arrangement The problem can be represented by the symbol m x n x k.
In this note we present a system (OR-Library) that distributes test problems by electronic mail (e-mail). This system currently has available test problems drawn from a number of different areas of operational research.
Consider scheduling n independent, single operation jobs, all available at time zero, on m identical processors. Further, assume that each job must be processed by exactly one of these processors, and it is desired to minimize makespan. This paper reports a computationally efficient procedure for treating this problem, which utilizes human ingenuity to improve on a traditional solution procedure. Computational experience with the procedure indicates that good solutions to large problems are easily obtained; in fact out of 240 test problems, the optimal solution was found in every case. The entire procedure is simple enough for a shop foreman to be able to solve large problems by hand.
A job scheduling problem is one of the most complicated and well-known combinatorial optimization problems. A previous space resource constrained job scheduling problem stated that the assembly process of a machine requires a certain amount of space on the shop floor within the factory for a period of time. The sizes of the shop floor and machines will determine the number of machines which can be assembled at the same time. There are a few research papers investigating space resource constrained job scheduling problems. In this study, we intend to find a schedule in order to minimize the makespan by converting the container loading problem heuristic into one that solves the space scheduling optimization problem. The processing time requirement for each job is the depth for each box in Pisinger's CLP heuristic. The testing data was obtained from the OR-Library and collected from a real company in central Taiwan during 2008. After validation, we find that our approach is more efficient than other well-known dispatching rules for obtaining the best schedule within the minimum makespan. We also verify that if a job completes early and moves into an unlimited buffer situation, it will generate the less makespan and maybe improve space utilization. We suggest that job height could be included into this problem in future studies.
The job-shop scheduling problem (JSSP) is a branch of production scheduling, and it is well known that this problem is NP-hard. Many different approaches have been applied to JSSP and a rich harvest has been obtained. However, some JSSP, even with moderate size, cannot be solved to guarantee optimality. The standard particle optimization algorithm generally is used to solve continuous optimization problems, and is used rarely to solve discrete problems such as JSSP. This paper presents a similar PSO algorithm to solve JSSP. At the same time, some new valid algorithm operators are proposed in this paper, and through simulation we find out the effectiveness of them. Three representative (Taillard) instances were made by computational experiments, through comparing the SPSO algorithm with standard GA, and we obtained that the SPSOA is more clearly efficacious than standard GA for JSSP to minimize makespan.
We consider the two uniform parallel machine problem with the objective of minimizing makespan. The problem can be transformed into a special problem of two identical parallel machines from the viewpoint of workload instead of completion time. An optimal algorithm is developed for the transformed special problem. Although the proposed algorithm has an exponential time complexity, the results show that it can find the optimal solution for large-sized problems in a short time.
The knapsack container loading problem is the problem of loading a subset of rectangular boxes into a rectangular container of fixed dimensions such that the volume of the packed boxes is maximized. A new heuristic based on the wall-building approach is proposed, which decomposes the problem into a number of layers which again are split into a number of strips. The packing of a strip may be formulated and solved optimally as a Knapsack Problem with capacity equal to the width or height of the container. The depth of a layer as well as the thickness of each strip is decided through a branch-and-bound approach where at each node only a subset of branches is explored.Several ranking rules for the selection of the most promising layer depths and strip widths are presented and the performance of the corresponding algorithms is experimentally compared for homogeneous and heterogeneous instances. The best ranking rule is then used in a comprehensive computational study involving large-sized instances. These computational results show that instances with a total box volume up to 90% easily may be solved to optimality, and that average fillings of the container volume exceeding 95% may be obtained for large-sized instances.
An important class of problems in manufacturing are those in which there is an item to be produced, a set of components which can be assembled together to produce the item, and a set of identical machines capable to perform the assembly operations. After discussing several optimality criteria, we address the problem in which we want to select a sequence of assembly operations (assembly plan), and schedule the selected operations on the machines, in such a way to minimize the makespan. This problem generalizes P|tree|Cmax, i.e., the minimum makespan machine scheduling problem with tree-type precedence constraints, where the list of operations to be scheduled is known a priori. We show that the problem can be quite naturally modelled making use of Directed Hypergraphs, and describe a general heuristic, showing that in a particular but still relevant case it yields solutions with a bounded relative error. Computational results are presented.
Job scheduling in machinery industry with space constrain. System Analysis Section
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Jobs scheduling in an assembly factory with space obstacles
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Application of scheduling technique to job space allocation problem in an assembly factory
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